What is the domain and range of the equation $$y=-2\sqrt{x+3}-1$$ ?

Domain: $$D: x \ge -3$$ ; Range: $$R: y \le -1$$ .

List all possible rational zeros of the polynomial function $$f(x) = 3x^5 - 5x^2 + x + 6$$ .

Possible rational zeros: $$\{1/3, 2/3, 1, 2, 3, 6, -1/3, -2/3, -1, -2, -3, -6\}$$ .

Find all the solutions of the polynomial equation $$x^4 - 3x^3 + 3x^2 - 3x + 2 = 0$$ .

Solutions: $$x = 1, x = 1, x = 1, x = 2$$ .

Graph the inequality $$y

The graph is below the curve of $$y = 2\sqrt{x}$$ .

What is the quadratic formula?

The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

Explain the concept of 'asymptote' in rational functions.

An asymptote is a line that a graph approaches but never touches.

What is the difference between a function and a relation?

A function is a relation where each input has exactly one output.

Define 'discriminant' in the context of quadratic equations.

The discriminant is $$D = b^2 - 4ac$$ ; it determines the nature of the roots.

What does it mean for a function to be 'increasing'?

A function is increasing if, for any two points $$x_1

What is the significance of the leading coefficient in a polynomial?

The leading coefficient determines the end behavior of the polynomial function.

Define 'completing the square'.

Completing the square is a method used to solve quadratic equations by rewriting them in vertex form.

What is the relationship between the roots and the factors of a polynomial?

The roots of a polynomial are the values of $$x$$ that make the polynomial equal to zero; they correspond to the factors of the polynomial.

Review for Test #12 - Algebra 2 Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

Back

2.

FLASHCARD QUESTION

Front

Write the equation of the square root function translated to have an endpoint at (4,-1) and vertically compressed by a factor of 1/3.

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the vertex form of a quadratic function?

Back

7.

FLASHCARD QUESTION

Front

Define the term 'rational function'.

Back

A rational function is a function that can be expressed as the quotient of two polynomials.

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